An interacting particle model and a Pieri-type formula for the orthogonal group

We introduce a new interacting particles model with blocking and pushing interactions. Particles evolve on the positive line jumping on their own volition rightwards or leftwards according to geometric jumps with parameter q. We show that the model involves a Pieri-type formula for the orthogonal group. We prove that the two extreme cases - q=0 and q=1 - lead respectively to a random tiling model studied by Borodin and Kuan and to a random matrix model.Comment: 1

Stochastic B\"acklund transformations

How does one introduce randomness into a classical dynamical system in order to produce something which is related to the `corresponding' quantum system? We consider this question from a probabilistic point of view, in the context of some integrable Hamiltonian systems

Methods to estimate aboveground wood productivity from long-term forest inventory plots

Forest inventory plots are widely used to estimate biomass carbon storage and its change over time. While there has been much debate and exploration of the analytical methods for calculating biomass, the methods used to determine rates of wood production have not been evaluated to the same degree. This affects assessment of ecosystem fluxes and may have wider implications if inventory data are used to parameterise biospheric models, or scaled to large areas in assessments of carbon sequestration. Here we use a dataset of 35 long-term Amazonian forest inventory plots to test different methods of calculating wood production rates. These address potential biases associated with three issues that routinely impact the interpretation of tree measurement data: (1) changes in the point of measurement (POM) of stem diameter as trees grow over time; (2) unequal length of time between censuses; and (3) the treatment of trees that pass the minimum diameter threshold (“recruits”). We derive corrections that control for changing POM height, that account for the unobserved growth of trees that die within census intervals, and that explore different assumptions regarding the growth of recruits during the previous census interval. For our dataset we find that annual aboveground coarse wood production (AGWP; in Mg ha−1 year−1 of dry matter) is underestimated on average by 9.2% if corrections are not made to control for changes in POM height. Failure to control for the length of sampling intervals results in a mean underestimation of 2.7% in annual AGWP in our plots for a mean interval length of 3.6 years. Different methods for treating recruits result in mean differences of up to 8.1% in AGWP. In general, the greater the length of time a plot is sampled for and the greater the time elapsed between censuses, the greater the tendency to underestimate wood production. We recommend that POM changes, census interval length, and the contribution of recruits should all be accounted for when estimating productivity rates, and suggest methods for doing this.European UnionUK Natural Environment Research CouncilGordon and Betty Moore FoundationCASE sponsorship from UNEP-WCMCRoyal Society University Research FellowshipERC Advanced Grant “Tropical Forests in the Changing Earth System”Royal Society Wolfson Research Merit Awar

Survival probability of mutually killing Brownian motions and the O'Connell process

Recently O'Connell introduced an interacting diffusive particle system in order to study a directed polymer model in 1+1 dimensions. The infinitesimal generator of the process is a harmonic transform of the quantum Toda-lattice Hamiltonian by the Whittaker function. As a physical interpretation of this construction, we show that the O'Connell process without drift is realized as a system of mutually killing Brownian motions conditioned that all particles survive forever. When the characteristic length of interaction killing other particles goes to zero, the process is reduced to the noncolliding Brownian motion (the Dyson model).Comment: v2: AMS-LaTeX, 20 pages, 2 figures, minor corrections made for publication in J. Stat. Phy

Phylogenetic diversity of Amazonian tree communities

This is the peer reviewed version of the following article: Honorio Coronado, E. N., Dexter, K. G., Pennington, R. T., Chave, J., Lewis, S. L., Alexiades, M. N., Alvarez, E., Alves de Oliveira, A., Amaral, I. L., Araujo-Murakami, A., Arets, E. J. M. M., Aymard, G. A., Baraloto, C., Bonal, D., Brienen, R., Cerón, C., Cornejo Valverde, F., Di Fiore, A., Farfan-Rios, W., Feldpausch, T. R., Higuchi, N., Huamantupa-Chuquimaco, I., Laurance, S. G., Laurance, W. F., López-Gonzalez, G., Marimon, B. S., Marimon-Junior, B. H., Monteagudo Mendoza, A., Neill, D., Palacios Cuenca, W., Peñuela Mora, M. C., Pitman, N. C. A., Prieto, A., Quesada, C. A., Ramirez Angulo, H., Rudas, A., Ruschel, A. R., Salinas Revilla, N., Salomão, R. P., Segalin de Andrade, A., Silman, M. R., Spironello, W., ter Steege, H., Terborgh, J., Toledo, M., Valenzuela Gamarra, L., Vieira, I. C. G., Vilanova Torre, E., Vos, V., Phillips, O. L. (2015), Phylogenetic diversity of Amazonian tree communities. Diversity and Distributions, 21: 1295–1307. doi: 10.1111/ddi.12357, which has been published in final form at 10.1111/ddi.12357Aim: To examine variation in the phylogenetic diversity (PD) of tree communities across geographical and environmental gradients in Amazonia. Location: Two hundred and eighty-three c. 1 ha forest inventory plots from across Amazonia. Methods: We evaluated PD as the total phylogenetic branch length across species in each plot (PDss), the mean pairwise phylogenetic distance between species (MPD), the mean nearest taxon distance (MNTD) and their equivalents standardized for species richness (ses.PDss, ses.MPD, ses.MNTD). We compared PD of tree communities growing (1) on substrates of varying geological age; and (2) in environments with varying ecophysiological barriers to growth and survival. Results: PDss is strongly positively correlated with species richness (SR), whereas MNTD has a negative correlation. Communities on geologically young- and intermediate-aged substrates (western and central Amazonia respectively) have the highest SR, and therefore the highest PDss and the lowest MNTD. We find that the youngest and oldest substrates (the latter on the Brazilian and Guiana Shields) have the highest ses.PDss and ses.MNTD. MPD and ses.MPD are strongly correlated with how evenly taxa are distributed among the three principal angiosperm clades and are both highest in western Amazonia. Meanwhile, seasonally dry tropical forest (SDTF) and forests on white sands have low PD, as evaluated by any metric. Main conclusions: High ses.PDss and ses.MNTD reflect greater lineage diversity in communities. We suggest that high ses.PDss and ses.MNTD in western Amazonia results from its favourable, easy-to-colonize environment, whereas high values in the Brazilian and Guianan Shields may be due to accumulation of lineages over a longer period of time. White-sand forests and SDTF are dominated by close relatives from fewer lineages, perhaps reflecting ecophysiological barriers that are difficult to surmount evolutionarily. Because MPD and ses.MPD do not reflect lineage diversity per se, we suggest that PDss, ses.PDss and ses.MNTD may be the most useful diversity metrics for setting large-scale conservation priorities.FINCyT - PhD studentshipSchool of Geography of the University of LeedsRoyal Botanic Garden EdinburghNatural Environment Research Council (NERC)Gordon and Betty Moore FoundationEuropean Union's Seventh Framework ProgrammeERCCNPq/PELDNSF - Fellowshi

Tree height integrated into pantropical forest biomass estimates

Copyright © 2012 European Geosciences Union. This is the published version available at http://www.biogeosciences.net/9/3381/2012/bg-9-3381-2012.htmlAboveground tropical tree biomass and carbon storage estimates commonly ignore tree height (H). We estimate the effect of incorporating H on tropics-wide forest biomass estimates in 327 plots across four continents using 42 656 H and diameter measurements and harvested trees from 20 sites to answer the following questions: 1. What is the best H-model form and geographic unit to include in biomass models to minimise site-level uncertainty in estimates of destructive biomass? 2. To what extent does including H estimates derived in (1) reduce uncertainty in biomass estimates across all 327 plots? 3. What effect does accounting for H have on plot- and continental-scale forest biomass estimates? The mean relative error in biomass estimates of destructively harvested trees when including H (mean 0.06), was half that when excluding H (mean 0.13). Power- and Weibull-H models provided the greatest reduction in uncertainty, with regional Weibull-H models preferred because they reduce uncertainty in smaller-diameter classes (≤40 cm D) that store about one-third of biomass per hectare in most forests. Propagating the relationships from destructively harvested tree biomass to each of the 327 plots from across the tropics shows that including H reduces errors from 41.8 Mg ha−1 (range 6.6 to 112.4) to 8.0 Mg ha−1 (−2.5 to 23.0). For all plots, aboveground live biomass was −52.2 Mg ha−1 (−82.0 to −20.3 bootstrapped 95% CI), or 13%, lower when including H estimates, with the greatest relative reductions in estimated biomass in forests of the Brazilian Shield, east Africa, and Australia, and relatively little change in the Guiana Shield, central Africa and southeast Asia. Appreciably different stand structure was observed among regions across the tropical continents, with some storing significantly more biomass in small diameter stems, which affects selection of the best height models to reduce uncertainty and biomass reductions due to H. After accounting for variation in H, total biomass per hectare is greatest in Australia, the Guiana Shield, Asia, central and east Africa, and lowest in east-central Amazonia, W. Africa, W. Amazonia, and the Brazilian Shield (descending order). Thus, if tropical forests span 1668 million km2 and store 285 Pg C (estimate including H), then applying our regional relationships implies that carbon storage is overestimated by 35 Pg C (31–39 bootstrapped 95% CI) if H is ignored, assuming that the sampled plots are an unbiased statistical representation of all tropical forest in terms of biomass and height factors. Our results show that tree H is an important allometric factor that needs to be included in future forest biomass estimates to reduce error in estimates of tropical carbon stocks and emissions due to deforestation

Evolutionary Heritage Influences Amazon Tree Ecology

Lineages tend to retain ecological characteristics of their ancestors through time. However, for some traits, selection during evolutionary history may have also played a role in determining trait values. To address the relative importance of these processes requires large-scale quantification of traits and evolutionary relationships among species. The Amazonian tree flora comprises a high diversity of angiosperm lineages and species with widely differing life-history characteristics, providing an excellent system to investigate the combined influences of evolutionary heritage and selection in determining trait variation. We used trait data related to the major axes of life-history variation among tropical trees (e.g. growth and mortality rates) from 577 inventory plots in closed-canopy forest, mapped onto a phylogenetic hypothesis spanning more than 300 genera including all major angiosperm clades to test for evolutionary constraints on traits. We found significant phylogenetic signal (PS) for all traits, consistent with evolutionarily related genera having more similar characteristics than expected by chance. Although there is also evidence for repeated evolution of pioneer and shade tolerant life-history strategies within independent lineages, the existence of significant PS allows clearer predictions of the links between evolutionary diversity, ecosystem function and the response of tropical forests to global change

Carbon uptake by mature Amazon forests has mitigated Amazon nations' carbon emissions

Background: Several independent lines of evidence suggest that Amazon forests have provided a significant carbon sink service, and also that the Amazon carbon sink in intact, mature forests may now be threatened as a result of different processes. There has however been no work done to quantify non-land-use-change forest carbon fluxes on a national basis within Amazonia, or to place these national fluxes and their possible changes in the context of the major anthropogenic carbon fluxes in the region. Here we present a first attempt to interpret results from groundbased monitoring of mature forest carbon fluxes in a biogeographically, politically, and temporally differentiated way. Specifically, using results from a large long-term network of forest plots, we estimate the Amazon biomass carbon balance over the last three decades for the different regions and nine nations of Amazonia, and evaluate the magnitude and trajectory of these differentiated balances in relation to major national anthropogenic carbon emissions. Results: The sink of carbon into mature forests has been remarkably geographically ubiquitous across Amazonia, being substantial and persistent in each of the five biogeographic regions within Amazonia. Between 1980 and 2010, it has more than mitigated the fossil fuel emissions of every single national economy, except that of Venezuela. For most nations (Bolivia, Colombia, Ecuador, French Guiana, Guyana, Peru, Suriname) the sink has probably additionally mitigated all anthropogenic carbon emissions due to Amazon deforestation and other land use change. While the sink has weakened in some regions since 2000, our analysis suggests that Amazon nations which are able to conserve large areas of natural and semi-natural landscape still contribute globally-significant carbon sequestration. Conclusions: Mature forests across all of Amazonia have contributed significantly to mitigating climate change for decades. Yet Amazon nations have not directly benefited from providing this global scale ecosystem service. We suggest that better monitoring and reporting of the carbon fluxes within mature forests, and understanding the drivers of changes in their balance, must become national, as well as international, priorities